Stoichiometry-based model

Figure 7.6 Hybrid dyiiamic/static simulation algorithm. Using flux-based methods, the algorithm allows dynamic models to be integrated with stoichiometry-based models.

The treatment above is site-based. It is useful when experiments provide all three quantities Ka, Kh, and Kc- But this amount of information is often not available. Notice that the terms Ka and Kb always appear as a sum Ka + Kh in Equation (28.7). If you use the binding constants as parameters to fit experimental data of v versus x, and if you have no additional information, you won t be able to choose Ka and Kb independently. You can only determine their sum, so you are only justified in using two independent parameters to fit the data, not three. The stoichiometry-based model in the next section uses only two parameters to describe the same two-site binding process. 

When this stoichiometry-based model fits your data, it is preferable to the site-based model because it requires one less parameter. Example 28.1 demonstrates both approaches. 

The hydrogen used in hydrotreating can be predicted from the set of equations given in Table 5, which are based on stoichiometry of model reactions. The formulas correspond to 1, 3, and 5 mol of hydrogen per mole of olefin, sulfur, and nitrogen, respectively. 

Based on the stoichiometry, we model the output of each of the reactors. For example, for reactor I... 

Molecular modeling seeks to answer questions about molecular properties— stabilities, reactivities, electronic properties—as they are related to molecular structure. The visualization and analysis of such structures, as well as their molecular properties and molecular interactions, are based on some theoretical means for predicting the structures and properties of molecules and complexes. If an algorithm can be developed to calculate a structure with a given stoichiometry and connectivity, one can then attempt to compute properties based on calculated molecular structure and vice versa. 

The semi-empirical descriptions of adsorbate/solid interactions are based on net changes in system composition and, unlike surface complexation models, do not explicitly identify the details of such interactions. Included in this group are distribution coefficients (Kp) and apparent adsorbate/proton exchange stoichiometries. Distribution coefficients are derived from the simple association reaction... 

Unfortunately, OH and O concentrations in flames are determined by detailed chemical kinetics and cannot be accurately predicted from simple equilibrium at the local temperature and stoichiometry. This is particularly true when active soot oxidation is occurring and the local temperature is decreasing with flame residence time [59], As a consequence, most attempts to model soot oxidation in flames have by necessity used a relation based on oxidation by 02 and then applied a correction factor to augment the rate to approximate the effect of oxidation by radicals. The two most commonly applied rate equations for soot oxidation by 02 are those developed by Lee el al. [61] and Nagle and Strickland-Constable [62],... 

Figure 35. Total conductivity, a, and oxygen stoichiometry, 3-d, at 1000 °C of Lao.9Sro.iMn03-(5, from measurements by Kuo et al. The model calculations are based on a large polaron model with equilibrium constants as given in ref 216. Thick line calculated stoichiometry, thin line calculated conductivity. (Reprinted with permission from ref 216. Copyright 2000 Elsevier.)...

The objectives of this project are consistent with the objectives (1) and (4) above. The general objective of this project has been to verify a new measurement method to analyse the thermochemical conversion of biofuels in the context of PBC, which is based on the three-step model mentioned above. The sought quantities of the method are the mass flow and stoichiometry of conversion gas, as well as air factors of conversion and combustion system. One of the specific aims of this project is to find a physical explanation why it is more difficult to obtain acceptable emissions from combustion of fuel wood than from for example wood pellets for the same conditions in a given PBC system. This project includes the following stages ... 

What the three-step model really points out is that it is theoretically correct to carry out basic combustion calculations for a PBC system based on the mass flow and stoichiometry of the conversion gas from the conversion system and not based on the mass flow of solid fuel entering the conversion system. The two-step model approach applied on a PBC system, which is equivalent to assuming that the conversion efficiency is 100 %, is a functional engineering approach, because the conversion efficiency is in many cases very close to unity. However, there are cases where the two-step model approach results in a physical conflict, for example the mass flows in PBC sysfem of batch type cannot be theoretically analysed with a two-step model. 

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